Vegetable Lasagna with White Sauce

Name: Vegetable Lasagna with White Sauce
Ingredients: 1 tablespoon extra-virgin olive oil; 1 cup chopped yellow onion; 2 large cloves garlic, finely chopped; 3 (10 ounce) packages frozen mixed vegetables (such as green beans, carrots, zucchini and yellow squash); ¼ cup chopped fresh basil, plus more for garnish; 3 tablespoons unsalted butter; 6 tablespoons all-purpose flour; 3 ½ cups whole milk; ½ cup grated Parmesan cheese; ¼ teaspoon salt; 1 (9 ounce) package no-boil lasagna noodles; 2 (12 ounce) packages frozen butternut squash puree, thawed; 4 cups shredded Italian cheese blend